Is it possible to have coordinate system with 3D cursor as origin?
Xavier, you can position a selection at a set of coordinates in the edit menu by using the 3D cursor location on the Properties menu N.
You can then move a selected point to the cursor location using the Snap menu Shift+S and selecting "Selection to Cursor"
This positions the selection using the global coordinate system.

You can also enter the coordinates of the active vertex directly using that same menu.

Beneath the coordinates, you  specify weather the location is in local or global coordinates.
You could then combine that with the cursor location.